Math, asked by royalaniket1234, 4 months ago

Solve by the method of substitution. ​

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Answers

Answered by prithapaul35
0

Answer:

this is the answer

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Answered by varadad25
0

Question:

Solve by the method of substitution.

( 5 / x ) + 3y = 8

( 4 / x ) + 10y = 56

Answer:

The solution of the given equations is

( x, y ) = ( - 19 / 44, 124 / 19 ).

Step-by-step-explanation:

The given linear equations are

( 5 / x ) + 3y = 8

⇒ ( 5 + 3xy ) / x = 8

⇒ 5 + 3xy = 8x

⇒ 3xy = 8x - 5

y = ( 8x - 5 ) / 3x - - - ( 1 ) &

( 4 / x ) + 10y = 56

⇒ ( 4 + 10xy ) / x = 56

⇒ 10xy + 4 = 56x

⇒ [ 10x ( 8x - 5 ) / 3x ] + 4 = 56x - - - [ From ( 1 ) ]

⇒ [ ( 80x² - 50x ) / 3x ] + 4 = 56x

⇒ ( 80x² - 50x + 12x ) / 3x = 56x

⇒ 80x² - 38x = 56x * 3x

⇒ 80x² - 38x = 168x²

⇒ 80x² - 38x - 168x² = 0

⇒ - 88x² - 38x = 0

⇒ - 2x ( 44x + 19 ) = 0

⇒ - 2x = 0 OR ( 44x + 19 ) = 0

⇒ x = - 0 / 2 OR 44x + 19 = 0

⇒ x = 0 OR 44x = - 19

x = 0 OR x = - 19 / 44

As x is in denominator in both equations,

x = 0 is unacceptable.

x = - 19 / 44

Now,

y = ( 8x - 5 ) / 3x - - - ( 1 )

⇒ y = [ ( 8 * - 19 / 44 ) - 5 ] / 3 * ( - 19 / 44 )

⇒ y = [ ( 2 * - 19 / 11 ) - 5 ] / ( - 57 / 44 )

⇒ y = [ ( - 38 / 11 ) - 5 ] / ( - 57 / 44 )

⇒ y = [ ( - 38 - 55 ) / 11 ] / ( - 57 / 44 )

⇒ y = ( - 93 / 11 ) / ( - 57 / 44 )

⇒ y = ( - 93 / 11 ) * ( - 44 / 57 )

⇒ y = ( - 93 * - 44 ) / ( 11 * 57 )

⇒ y = ( 93 / 57 ) * ( 44 / 11 )

⇒ y = ( 31 / 19 ) * 4

⇒ y = 124 / 19

The solution of the given equations is

( x, y ) = ( - 19 / 44, 124 / 19 ).

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